Question

1. the two triangles below are similar. solve for x.

Explanation:

Step1: Identify similar triangles ratio

Since triangles \(ABC\) and \(DEC\) are similar, their corresponding sides are proportional. So \(\frac{AB}{DE}=\frac{BC}{EC}\).
Given \(AB = 13\) ft, \(DE = 5\) ft, \(EC = 11\) ft, \(BC = x\). So \(\frac{13}{5}=\frac{x}{11}\).

Step2: Solve for \(x\)

Cross - multiply: \(5x=13\times11\).
Calculate \(13\times11 = 143\), so \(5x = 143\).
Then \(x=\frac{143}{5}=28.6\).

Answer:

\(28.6\) feet